Summary: Mathematics 3C Summer 2009
Worksheet 5, August 20th, TA Grace Kennedy
1. Suppose salt water having a concentration of 2 grams of salt per liter of
water is entering a 200-liter vat of fresh water at 5 liters per minute. The
salt water mixes in with the fresh water and the brine exits by a funnel at
the bottom at the same rate that the salt water is being poured in.
(a) Set up the IVP describing the amount of salt Q(t) (in grams) in the
vat at time t minutes.
(b) Solve for Q(t).
(c) What is the long-term behaviour for Q(t)? In other words, what
happens as time goes on? Is this surprising?
2. There are 95 students in your 3C class. Suppose Rob and Garrett, who
will sub for Grace's sections on Tues., 9/8 decide it is funny to start a
rumor that the final exam on the 10th is canceled. They tell all 40 of
Grace's students. Initially, only Sonja's students know the truth.
Let y(t) be the number of students who think there is no exam after
t days. The rate at which the number of students who think there is no
exam grows proportionally to the number of students who know the rumor